diff --git a/src/anthem/Simplification.cpp b/src/anthem/Simplification.cpp
index 90abea3..e162fdb 100644
--- a/src/anthem/Simplification.cpp
+++ b/src/anthem/Simplification.cpp
@@ -1,5 +1,7 @@
 #include <anthem/Simplification.h>
 
+#include <iostream>
+
 namespace anthem
 {
 
@@ -11,75 +13,196 @@ namespace anthem
 
 bool isPrimitiveTerm(const ast::Term &term)
 {
-	const auto binaryOperationIsNotPrimitiveTerm =
+	const auto handleBinaryOperation =
 		[](const ast::BinaryOperationPointer &)
 		{
 			return false;
 		};
 
-	const auto intervalIsNotPrimitiveTerm =
+	const auto handleInterval =
 		[](const ast::IntervalPointer &)
 		{
 			return false;
 		};
 
-	const auto defaultIsPrimitiveTerm =
+	const auto handleDefault =
 		[](const auto &)
 		{
 			return true;
 		};
 
-	return term.match(binaryOperationIsNotPrimitiveTerm, intervalIsNotPrimitiveTerm, defaultIsPrimitiveTerm);
+	return term.match(handleBinaryOperation, handleInterval, handleDefault);
 }
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
-ast::Formula simplifyFormula(ast::Formula &&formula)
+bool matchesVariable(const ast::Term &term, const ast::VariablePointer &variable)
 {
-	const auto simplifyAnd =
+	const auto handleVariable =
+		[&](const ast::VariablePointer &other)
+		{
+			return variable->name == other->name;
+		};
+
+	const auto handleDefault =
+		[](const auto &)
+		{
+			return false;
+		};
+
+	return term.match(handleVariable, handleDefault);
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+std::experimental::optional<ast::Term> extractAssignedTerm(ast::Formula &formula, const ast::VariablePointer &variable)
+{
+	const auto handleComparison =
+		[&](ast::ComparisonPointer &comparison) -> std::experimental::optional<ast::Term>
+		{
+			if (comparison->operator_ != ast::Comparison::Operator::Equal)
+				return std::experimental::nullopt;
+
+			if (matchesVariable(comparison->left, variable))
+				return std::move(comparison->right);
+
+			if (matchesVariable(comparison->right, variable))
+				return std::move(comparison->left);
+
+			return std::experimental::nullopt;
+		};
+
+	const auto handleDefault =
+		[](auto &) -> std::experimental::optional<ast::Term>
+		{
+			return std::experimental::nullopt;
+		};
+
+	return formula.match(handleComparison, handleDefault);
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+ast::Formula simplify(ast::ExistsPointer &exists)
+{
+	if (!exists->argument.is<ast::AndPointer>())
+		return std::move(exists);
+
+	auto &conjunction = exists->argument.get_unchecked<ast::AndPointer>();
+	auto &arguments = conjunction->arguments;
+
+	// Check that formula is in normal form
+	if (!arguments.back().is<ast::PredicatePointer>())
+		return std::move(exists);
+
+	const auto replaceVariableInPredicateWithTerm =
+		[](ast::PredicatePointer &predicate, const ast::VariablePointer &variable, ast::Term &&term)
+		{
+			for (auto &argument : predicate->arguments)
+			{
+				if (!matchesVariable(argument, variable))
+					continue;
+
+				argument = std::move(term);
+				break;
+			}
+		};
+
+	// Simplify formulas of type “exists X (X = t and F(Y))” to “F(t)”
+	for (auto i = exists->variables.begin(); i != exists->variables.end();)
+	{
+		auto &variable = *i;
+
+		bool wasVariableReplaced = false;
+
+		for (auto j = arguments.begin(); j != arguments.end(); j++)
+		{
+			auto &argument = *j;
+			auto assignedTerm = extractAssignedTerm(argument, variable);
+
+			if (!assignedTerm)
+				continue;
+
+			auto &lastArgument = arguments.back().get_unchecked<ast::PredicatePointer>();
+
+			// If this argument is an assignment of the variable to some other term, remove the assignment and replace the variable with the other term
+			replaceVariableInPredicateWithTerm(lastArgument, variable, std::move(assignedTerm.value()));
+
+			arguments.erase(j);
+			wasVariableReplaced = true;
+			break;
+		}
+
+		if (wasVariableReplaced)
+		{
+			i = exists->variables.erase(i);
+			continue;
+		}
+
+		i++;
+	}
+
+	if (exists->variables.empty())
+	{
+		assert(!conjunction->arguments.empty());
+
+		if (conjunction->arguments.size() == 1)
+			return std::move(conjunction->arguments.front());
+
+		return std::move(exists->argument);
+	}
+
+	return std::move(exists);
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+ast::Formula simplify(ast::Formula &&formula)
+{
+	const auto handleAnd =
 		[&](ast::AndPointer &and_) -> ast::Formula
 		{
 			for (auto &argument : and_->arguments)
-				argument = simplifyFormula(std::move(argument));
+				argument = simplify(std::move(argument));
 
 			return std::move(and_);
 		};
 
-	const auto simplifyBiconditional =
+	const auto handleBiconditional =
 		[&](ast::BiconditionalPointer &biconditional) -> ast::Formula
 		{
-			biconditional->left = simplifyFormula(std::move(biconditional->left));
-			biconditional->right = simplifyFormula(std::move(biconditional->right));
+			biconditional->left = simplify(std::move(biconditional->left));
+			biconditional->right = simplify(std::move(biconditional->right));
 
 			return std::move(biconditional);
 		};
 
-	const auto simplifyExists =
+	const auto handleExists =
 		[&](ast::ExistsPointer &exists) -> ast::Formula
 		{
-			exists->argument = simplifyFormula(std::move(exists->argument));
+			exists->argument = simplify(std::move(exists->argument));
 
-			return std::move(exists);
+			return simplify(exists);
 		};
 
-	const auto simplifyForAll =
+	const auto handleForAll =
 		[&](ast::ForAllPointer &forAll) -> ast::Formula
 		{
-			forAll->argument = simplifyFormula(std::move(forAll->argument));
+			forAll->argument = simplify(std::move(forAll->argument));
 
 			return std::move(forAll);
 		};
 
-	const auto simplifyImplies =
+	const auto handleImplies =
 		[&](ast::ImpliesPointer &implies) -> ast::Formula
 		{
-			implies->antecedent = simplifyFormula(std::move(implies->antecedent));
-			implies->consequent = simplifyFormula(std::move(implies->consequent));
+			implies->antecedent = simplify(std::move(implies->antecedent));
+			implies->consequent = simplify(std::move(implies->consequent));
 
 			return std::move(implies);
 		};
 
-	const auto simplifyIn =
+	const auto handleIn =
 		[](ast::InPointer &in) -> ast::Formula
 		{
 			if (!isPrimitiveTerm(in->element) || !isPrimitiveTerm(in->set))
@@ -89,37 +212,30 @@ ast::Formula simplifyFormula(ast::Formula &&formula)
 			return std::make_unique<ast::Comparison>(ast::Comparison::Operator::Equal, std::move(in->element), std::move(in->set));
 		};
 
-	const auto simplifyNot =
+	const auto handleNot =
 		[&](ast::NotPointer &not_) -> ast::Formula
 		{
-			not_->argument = simplifyFormula(std::move(not_->argument));
+			not_->argument = simplify(std::move(not_->argument));
 
 			return std::move(not_);
 		};
 
-	const auto simplifyOr =
+	const auto handleOr =
 		[&](ast::OrPointer &or_) -> ast::Formula
 		{
 			for (auto &argument : or_->arguments)
-				argument = simplifyFormula(std::move(argument));
+				argument = simplify(std::move(argument));
 
 			return std::move(or_);
 		};
 
-	const auto defaultDoNothing =
+	const auto handleDefault =
 		[&](auto &x) -> ast::Formula
 		{
 			return std::move(x);
 		};
 
-	return formula.match(simplifyAnd, simplifyBiconditional, simplifyExists, simplifyForAll, simplifyImplies, simplifyIn, simplifyNot, simplifyOr, defaultDoNothing);
-}
-
-////////////////////////////////////////////////////////////////////////////////////////////////////
-
-ast::Formula simplify(ast::Formula &&formula)
-{
-	return simplifyFormula(std::move(formula));
+	return formula.match(handleAnd, handleBiconditional, handleExists, handleForAll, handleImplies, handleIn, handleNot, handleOr, handleDefault);
 }
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////